Quadrilateral relationships: Trapezoids and parallelograms

- [Instructor] So we're asked
to complete the statement

with always, sometimes or never.

And it says, "A trapezoid
is blank a parallelogram."

And this is a screenshot
from Khan Academy.

So is a trapezoid always a parallelogram,

is it sometimes a parallelogram

or is it never a parallelogram?

So pause this video and have a go at this

before we do this together.

Okay, so let's just think about

how these relate to each other.

So the definition of a trapezoid

that we are using on Khan Academy,

this is oftentimes called

the inclusive definition of a trapezoid,

is at least, at least,

one pair, pair,

of parallel, parallel sides.

So what are examples

based on that definition of a trapezoid?

Well, you could have a
trapezoid that looks like this.

So let's say that side
is parallel to that side.

So that's one pair of parallel sides

and a lot of people when
they think about a trapezoid,

they oftentimes think
about something like this

that has only one pair of parallel sides.

If we made that the definition,

that would be the exclusive definition.

But we're saying at least one pair

of parallel sides.

So it can also have two
pairs of parallel sides.

So we could also have this.

So let's say that's our first pair

of parallel sides right there,

but then we could also
have our second pair

of parallel sides.

Pair of parallel sides,
that's a tongue twister.

So that's our second pair.

And this right over
here is a parallelogram.

So a parallelogram has two
pairs of parallel sides,

but that meets the inclusive
definition of a trapezoid

that has at least one
pair of parallel sides.

So a parallelogram is always
going to be a trapezoid

by this definition, but
that's not the order here.

They're saying a trapezoid.

Well, sometimes it's not a parallelogram,

but sometimes a trapezoid
is a parallelogram.

So what we want to go with
this one is sometimes,

a trapezoid is sometimes a parallelogram.

We see that right over here.

This is not a parallelogram on the left,

this is a parallelogram on the right,

but these are both trapezoids.